Details

analyze169.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample75.0ms (1.8%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.1b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series105.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

43.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
35.0ms	(pow.f64 (hypot.f64 a b) 4)
14.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))

simplify118.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
417×	`fma-neg_binary64`
408×	`associate-+l+_binary64`
315×	`cancel-sign-sub-inv_binary64`
250×	`exp-prod_binary64`

Counts

159 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	3218
1	364	2814
2	1065	2628
3	3367	2622
4	4754	2618
5	4990	2618

prune188.0ms (4.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	137	5	142

Error

Counts

142 → 5

Alt Table

Status	Error	Program
	0.4b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))) -1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
	10.8b	(+.f64 (fma.f64 4 (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
	2.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 2 (.f64 a a) 4) (fma.f64 b b (.f64 a -12))))) (pow.f64 a 4)) -1)

Compiler

Compiled 4263 to 2372 computations (44.4% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))
	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	2.2b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series44.0ms (1%)

Counts

2 → 24

Calls

2 calls:

33.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))

11.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
16×	`unswap-sqr_binary64`
14×	`unpow-prod-down_binary64`
14×	`add-exp-log_binary64`
10×	`sqr-pow_binary64`

Counts

2 → 63

Calls

2 calls:

6.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

0.0ms

(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

746×	`distribute-rgt-in_binary64`
701×	`fma-def_binary64`
420×	`associate-+l+_binary64`
232×	`associate-+r+_binary64`
218×	`*-commutative_binary64`

Counts

87 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1938
1	297	1757
2	929	1569
3	2990	1514
4	5413	1514

prune278.0ms (6.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Error

Counts

182 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
	11.7b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
	2.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 7121 to 4477 computations (37.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4))
✓	0.0b	(.f64 a (-.f64 (.f64 2 a) 12))
✓	0.0b	(*.f64 a (fma.f64 a a a))
✓	1.6b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 2 a) 12))))

series61.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

29.0ms	(+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4))
26.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 2 a) 12))))
3.0ms	(*.f64 a (fma.f64 a a a))
3.0ms	(.f64 a (-.f64 (.f64 2 a) 12))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 101

Calls

4 calls:

10.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (.f64 2 a) 12))))
6.0ms	(.f64 a (-.f64 (.f64 2 a) 12))
5.0ms	(+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4))
3.0ms	(*.f64 a (fma.f64 a a a))

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
574×	`associate-+l+_binary64`
379×	`associate-+r+_binary64`
260×	`associate-l_binary64`
244×	`+-commutative_binary64`

Counts

173 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4061
1	579	3056
2	2027	2979
3	4493	2979
4	5077	2979

prune294.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	196	4	200

Error

Counts

200 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
	11.7b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
▶	2.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 7550 to 4456 computations (41% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))))
	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	3.1b	(exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))
✓	22.8b	(log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))

series334.0ms (7.8%)

Counts

3 → 72

Calls

3 calls:

307.0ms	(log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))
15.0ms	(exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))
12.0ms	(fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
9×	`add-exp-log_binary64`
6×	`exp-prod_binary64`
6×	`log-pow_binary64`
6×	`pow-prod-down_binary64`

Counts

3 → 43

Calls

3 calls:

9.0ms	(exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))
3.0ms	(log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))))

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-neg_binary64`
418×	`sub-neg_binary64`
304×	`fma-def_binary64`
216×	`unsub-neg_binary64`
162×	`associate-+l+_binary64`

Counts

115 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2013
1	285	1652
2	835	1635
3	3134	1635
4	4691	1635
5	4998	1635
6	4936	1635

prune178.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Error

Counts

151 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (.f64 a (fma.f64 a a a)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (-.f64 (*.f64 2 a) 12))))) (pow.f64 a 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
	11.7b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	2.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (exp.f64 (log.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 4545 to 2592 computations (43% saved)

regimes866.0ms (20.3%)

Accuracy

Total 0.0b remaining (79.2%)

Threshold costs 0.0b (79.2%)

Counts

138 → 1

Compiler

Compiled 18825 to 12777 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	23	43
2	23	43

end1.0ms (0%)

Compiler: Compiled 32 to 23 computations (28.1% saved)

sample1.0s (24.6%)

Algorithm

1×

intervals

Results

675.0ms	8000×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 185 to 127 computations (31.4% saved)

Details

analyze169.0ms (4%)

sample75.0ms (1.8%)

simplify60.0ms (1.4%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series105.0ms (2.5%)

rewrite9.0ms (0.2%)

simplify118.0ms (2.8%)

prune188.0ms (4.4%)

localize22.0ms (0.5%)

series44.0ms (1%)

rewrite10.0ms (0.2%)

simplify80.0ms (1.9%)

prune278.0ms (6.5%)

localize16.0ms (0.4%)

series61.0ms (1.4%)

rewrite29.0ms (0.7%)

simplify107.0ms (2.5%)

prune294.0ms (6.9%)

localize18.0ms (0.4%)

series334.0ms (7.8%)

rewrite14.0ms (0.3%)

simplify119.0ms (2.8%)

prune178.0ms (4.2%)

regimes866.0ms (20.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (24.6%)

Profiling